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GATE Mathematics 2014 Paper

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Question : 26

Total: 55

Let X be a set with at least two elements. Let τ‌and‌τ′ be two topologies on X such that τ′≠{ϕ,X}. Which of the following conditions is necessary for the identity function id : (X,τ)→(X,τ′) to be continuous?

τ⊆τ′
τ′⊆τ
no conditions on τ‌and‌τ′
τ∩τ′={Ø,X}

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